{"id":"b6d90877-af7a-470e-b99e-1a873454369b","arxiv_id":"2501.14912","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"Enforcing per-sample loss bounds during training yields more concentrated loss distributions than average-loss training, but the effect varies by task and needs careful tuning of a new threshold.","lead":"This paper proposes training neural networks by requiring a low loss on every training sample, instead of minimizing the average loss. The trade-off is a small drop in average performance for fewer very bad predictions, which matters when individual failures carry high cost.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The paper's own CIFAR10 results contradict the headline tail-behavior claim: FL/RFL have higher test Max CE than ERM and ERM has lower CVaR, so the universal claim lacks support.","rationale":"The reader's weakest assumption identifies transfer of training-set tail compression to the test distribution. That is indeed unsupported, but the paper has a more direct problem: on CIFAR10 even the training-set tail is not compressed relative to ERM (Table 7 and Figure 5). This is an internal inconsistency between the headline claim and the paper's own reported results, not merely a missing generalization guarantee. The reader's conditional verdict still seems appropriate because the paper contains valuable non-empirical contributions: the RFL-to-CSERM equivalence (Proposition 2), the primal-dual algorithm, and the informative failure mode of FL on infeasible problems. However, the central empirical claim must be scoped or the abstract and conclusion require revision. A straightforward recomputation from the released code would settle whether the contradictory numbers are reproducible and whether the 'consistently lower CVaR' claim can survive even on CIFAR10. I agree with the reader that the claim is overstated, but I would ground the critique in the in-paper contradiction rather than in the transfer question alone.","tokens_in":23156,"tokens_out":3259,"duration_ms":31111,"concrete_test":"Run the released code (github.com/juan43ramirez/feasible-learning) with the exact CIFAR10 settings of Table 7 and Figure 5 across the 5 seeds, and compute test-set CVaR at quantiles 0.5-0.95 with confidence intervals. If FL/RFL's test Max CE and CVaR remain above ERM's as reported, the Abstract and Section 5.3 must be revised to state that FL improves tail behavior only on some tasks, and the 'consistently' claim should be removed.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The load-bearing issue is not a subtle generalization gap; the paper's own CIFAR10 experiment breaks the headline claim even on the training set. In Table 7, ERM's train Max CE is 2.369 +/- 0.647 versus FL's 3.084 +/- 1.064, and test Max CE is 12.830 +/- 0.443 versus FL's 15.533 +/- 0.642; RFL is similar or worse. Appendix C.1 explicitly states: 'In training, we observe slightly better CDF and CVaR curves for ERM compared to FL and RFL... A similar trend is observed in the test set.' This directly contradicts the Section 5.3 sentence 'FL consistently achieves lower CVaR values compared to ERM' and the Abstract's unconditional 'improved tail behavior compared to ERM.' No distributional argument is offered to explain why constraints on training losses should transfer to test losses, but the failure is more basic: on CIFAR10 the constraints do not even produce a more concentrated training-loss distribution with the reported hyperparameters. The claim therefore survives only if it is scoped per-task; as written it is internally inconsistent with the paper's own results.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper introduces Feasible Learning (FL), a training paradigm in which a model is found by solving a feasibility problem that requires the per-sample loss to stay below a threshold epsilon, and Resilient Feasible Learning (RFL), a relaxation that adds minimal-norm slack variables to restore feasibility. The authors prove that RFL is equivalent to a quadratically regularized min-max problem (Proposition 1) and to a clamped-and-squared ERM objective (Proposition 2), and they propose alternating primal-dual updates with per-sample Lagrange multipliers. Experiments are reported on CIFAR10 classification, UTKFace age regression, and DPO fine-tuning of Llama-3.1-8B and Zephyr-3B. The central empirical claim is that FL and RFL achieve average performance comparable to ERM while improving tail behavior, i.e., reducing the number of very-high-loss samples and lowering CVaR.","tokens_in":23420,"tokens_out":5312,"duration_ms":59564,"significance":"The conceptual contribution is attractive and timely: framing learning as sample-level constraint satisfaction is a clean idea, and the primal-dual implementation is practical and has training cost comparable to ERM. The two propositions are simple but correctly proven, the slack-based treatment of infeasibility is principled, and the release of code supports reproducibility. The experiments span three qualitatively different tasks. However, the paper's most prominent advertised conclusion — that FL consistently yields less heavy-tailed loss distributions than ERM — is directly contradicted by the paper's own CIFAR10 results. Since this tail-behavior claim is the main reason a reader would prefer FL over ERM, the empirical core needs revision before the paper can be accepted in its current form.","major_comments":[{"comment":"The statement in Section 5.3 that 'FL consistently achieves lower CVaR values compared to ERM' and the conclusion that 'FL yields a less heavy-tailed loss distribution than ERM' are not supported by the paper's own CIFAR10 results. Appendix C.1 explicitly states: 'In training, we observe slightly better CDF and CVaR curves for ERM compared to FL and RFL... A similar trend is observed in the test set.' Table 7 reports ERM test Max CE 12.830 ± 0.443 versus FL 15.533 ± 0.642 and RFL 16.235 ± 1.510, and Figure 5 shows ERM below FL and RFL in the CIFAR10 CVaR curves. Because the abstract and Section 5.3 present tail improvement as a general property, this internal contradiction is load-bearing. The authors should either scope the tail-behavior claim to the DPO and UTKFace settings, or provide a criterion for when the effect holds (noting, for example, that RFL with α=10^-3 in Table 8 does produce a lower CIFAR10 test Max CE than ERM, unlike the α=1 configuration emphasized in the main text).","section":"§5.3, Abstract, Conclusion vs. Appendix C.1"},{"comment":"The paper provides no distributional argument or stated assumption under which training-set loss concentration transfers to the test set. Because FL's constraints are enforced only on training samples, the test-side tail improvement is an empirical pattern rather than a consequence of the formulation. Given the CIFAR10 counterexample, the authors should either state a concrete hypothesis or condition for when tail improvement transfers, or explicitly limit the empirical contribution to the tasks and configurations where the effect is observed.","section":"§5.3 and Appendix C"}],"minor_comments":[{"comment":"The text refers to 'a training dataset of 60000 samples,' but Table 3 lists CIFAR10 training size as 50000; please reconcile these numbers.","section":"Appendix C.1"},{"comment":"The DPO results are reported without error bars or an explicit statement of the number of seeds, despite Section 5 saying that 'unless stated otherwise, all reported metrics are averaged over 5 seeds'; please clarify whether the DPO runs are single-seed.","section":"Table 13"},{"comment":"The caption says the figure shows 'the loss and multiplier values' for UTKFace samples, but the figure appears to display only images; please describe how the loss and multiplier values are visualized.","section":"Figure 4"},{"comment":"There are minor typos ('Correspondance', 'Pennislvania'); please proofread.","section":"Title page and acknowledgements"},{"comment":"The sentence 'Once a constraint is strictly satisfied, the dual updates reduce the corresponding multiplier' is slightly imprecise, since the reduction happens in the gradient-ascent update only if the constraint remains satisfied; consider rewording for precision.","section":"§2.1"}],"recommendation":"major_revision","confidential_remarks":"The main issue is the internal contradiction between the general tail-behavior claims in the abstract, Section 5.3, and the conclusion, and the CIFAR10 results in Appendix C.1. I believe this is fixable by rescoping the claims and adding a discussion of when the effect does and does not appear. The paper's own scope paragraph already disclaims universal outperformance, so the authors have the material to make the manuscript consistent. I would also suggest that the reviewers check the related-work discussion for balanced coverage of alternative objectives such as CVaR minimization and distributionally robust optimization, since those are closely related to the tail-behavior claims but receive limited discussion."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Jean, quick take on arXiv:2501.14912 (Feasible Learning). The framework is more interesting than the title suggests: posing learning as a feasibility problem with per-sample loss constraints, and using Lagrange multipliers as dynamic reweighting, is a genuinely different framing from ERM. The RFL relaxation is clean, and the equivalence to CSERM and to a strongly-concave min-max problem (Propositions 1 and 2) is correct and useful. The code is public, and the experiments span classification, regression, and DPO. That part deserves a serious referee.\n\nBut the headline empirical claim does not survive contact with the paper's own appendix. The abstract says FL 'displays improved tail behavior compared to ERM' without qualification, and Section 5.3 says FL 'consistently achieves lower CVaR values' across tasks. Appendix C.1, for CIFAR10, says ERM has slightly better CDF and CVaR curves in training and a similar trend on test. Table 7 backs that up: FL test Max CE is 15.5±0.6 versus ERM's 12.8±0.4, and RFL is similar. This is not a subtle generalization gap. On this task, FL does not compress the training-loss tail either. The claim only works if it is scoped per-task, and even then CIFAR10 is a counterexample.\n\nThe DPO section has its own problems. Table 13 and Figures 9-10 compare ERM vs RFL, not FL, yet the text and Figure 2 label the method FL. There are no error bars for the LLM runs. The paper's own Section 5.2 admits that finding good α can require extensive tuning, which undercuts the robustness story.\n\nWhat the paper does well: the multiplier visualization on Two-Moons is illuminating, and the UTKFace outlier detection with multipliers is a nice observation. The authors explicitly state in the Scope that they do not claim FL outperforms ERM, which makes the abstract's unconditional claim feel like an editing slip rather than deliberate overreach. But it is a load-bearing slip, because the tail-behavior claim is the paper's main selling point.\n\nWho should read this: anyone working on constrained optimization for deep learning or on training objectives that target per-sample worst-case performance. The theory is worth citing. But the empirical section needs a careful revision: per-task claims with error bars, a clear statement of which method (FL or RFL) produced each figure, and an honest discussion of when tail compression happens and when it doesn't. If those fixes are made, this could be a useful paper.\n\nRecommendation: send it to peer review, but expect heavy revision. Don't desk reject; the framework is too clean to ignore.","headline":"A genuinely interesting learning framework with a clean theory, but its own CIFAR10 results contradict the abstract's unconditional tail-behavior claim.","tokens_in":23975,"tokens_out":2743,"would_cite":true,"duration_ms":24368,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"The paper argues that training models to cap each sample's loss, not minimize the average, produces fewer very-high-loss predictions at little average-cost penalty.","keywords":["Feasible Learning","per-sample loss constraints","primal-dual optimization","Resilient Feasible Learning","tail behavior","Conditional Value at Risk","preference optimization","constrained learning"],"falsifier":"Run FL and ERM on the same benchmarks with matched hyperparameter budgets and compare test-set Conditional Value at Risk at high quantiles; if FL does not beat ERM on held-out data in a majority of tasks, the paper's central claim fails. The CIFAR10 experiment in Appendix C is already one such comparison that does not go FL's way.","tokens_in":22975,"feed_emoji":"🎯","tokens_out":9186,"duration_ms":72109,"temperature":0.7,"pith_summary":"Feasible Learning (FL) replaces the usual objective of minimizing average loss with a feasibility problem: find a model whose loss on every training sample is below a threshold. Because any model meeting the constraints is acceptable, the optimization algorithm itself shapes the solution, and the paper studies a primal-dual method that re-weights samples through Lagrange multipliers. To handle thresholds that make the problem infeasible, the paper introduces Resilient Feasible Learning (RFL), which relaxes constraints with minimal-norm slack variables. Across image classification, age regression, and LLM preference optimization, the paper reports that FL- and RFL-trained models keep average performance close to ERM while producing a less heavy-tailed loss distribution. The central claim is that per-sample constraints, not average loss, are a viable organizing principle for training, with tail behavior as the payoff.","feed_headline":"Per-sample loss caps yield fewer very bad predictions","feed_subtitle":"Feasible Learning enforces per-sample loss caps, giving fewer extreme test errors at small average cost.","key_machinery":"The mechanism is the per-sample loss constraint: FL solves $\\min_{\\theta} 0$ subject to $g_i(\\theta) \\le \\epsilon$ for every training sample, where $g_i$ is the loss on sample $i$. The paper solves this through a Lagrangian game with one multiplier $\\lambda_i$ per sample; gradient descent on $\\theta$ with ascent on $\\lambda$ re-weights samples by their historical difficulty, so hard samples dominate updates and easy samples receive little pressure once their constraint is satisfied. RFL adds slack variables $u \\ge 0$ with an $\\alpha\\|u\\|^2$ penalty, which Proposition 1 turns into a quadratically regularized Lagrangian and Proposition 2 equates to an ERM objective with clamped-and-squared loss. The machinery's work is to make constraint satisfaction tractable at neural-network scale and to let the optimizer select a non-interpolating solution.","core_discovery":"On its own terms, the paper's central claim is that models trained by solving a feasibility problem with per-sample loss constraints display improved tail behavior compared to ERM, with only a marginal impact on average performance. In Section 5.3, the paper reports that FL consistently achieves lower Conditional Value at Risk (CVaR), the average loss among the highest-loss samples, than ERM on the DPO task, and the conclusion states that FL yields a less heavy-tailed loss distribution than ERM. The paper presents this as an empirical discovery supported across image classification, age regression, and language-model preference alignment, not as a universal theorem.","pith_inferences":["Beyond the paper: if the tail-compression effect generalizes, final multiplier magnitudes could be used as a data-quality score to flag mislabeled or duplicated examples, extending the paper's UTKFace illustration.","Beyond the paper: the paper's own CIFAR10 appendix shows the claim is not universal, so the immediate next experiment is a systematic comparison of training-set tail compression against test-set tail compression across benchmarks.","Beyond the paper: because RFL is equivalent to a clamped-and-squared ERM objective, existing theory for thresholded losses likely applies to FL's generalization, a connection the paper does not develop."],"forward_implications":["If the central claim holds, practitioners can train high-capacity models with per-sample loss caps at roughly ERM's computational cost and obtain test solutions with fewer extreme losses.","RFL gives a concrete recipe for infeasible settings: relax the constraints with minimal-norm slacks, which is equivalent to minimizing a clamped-and-squared loss, so standard ERM machinery can be reused.","The per-sample Lagrange multipliers carry a difficulty signal, so the final training run can identify hard or mislabeled examples, and the many zero multipliers suggest data pruning is possible.","In preference alignment for LLMs, RFL reduced maximum DPO losses while raising average loss only slightly, making it a candidate for deployments where a few bad responses matter more than average reward."],"supporting_citations":[{"why":"Supplies the gradient descent-ascent template for solving the FL Lagrangian game.","marker":"Arrow et al., 1958"},{"why":"Provides convergence guarantees for alternating gradient descent-ascent, the update scheme FL uses.","marker":"Zhang et al., 2022"},{"why":"Gives convergence guarantees for nonconvex-strongly-concave minimax problems that justify RFL's quadratically regularized Lagrangian.","marker":"Lin et al., 2020"},{"why":"Supplies the linear convergence rate used when the loss geometry is strongly convex.","marker":"Chen & Rockafellar, 1997"},{"why":"Introduces the slack-variable resilience idea that RFL adapts to a constant-objective feasibility problem.","marker":"Hounie et al., 2024"},{"why":"Provides the thresholded-loss regression baseline that RFL's clamped-and-squared formulation generalizes.","marker":"Vapnik, 1998"},{"why":"Defines the DPO objective used in the preference-optimization experiment.","marker":"Rafailov et al., 2024"},{"why":"Motivates why the optimizer's implicit bias matters when many solutions fit the data, the premise behind FL's algorithmic focus.","marker":"Soudry et al., 2018"}],"fun_headline_variants":["Per-sample loss caps cut extreme errors with tiny average cost","Worst-case errors shrink via per-sample loss caps","Per-sample constraints tame tail losses, small average cost","Better worst-case predictions for a marginal average cost"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing assumption is that compressing the high-loss tail on the training set also compresses it on fresh test data drawn from the same distribution; the paper's own CIFAR10 appendix shows one case where ERM has lower test tail losses than FL, so this transfer is not guaranteed.","fun_headline_variants_meta":{"raw":{"variants":["Per-sample loss caps cut extreme errors with tiny average cost","Worst-case errors shrink via per-sample loss caps","Per-sample constraints tame tail losses, small average cost","Better worst-case predictions for a marginal average cost"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001203,"raw_usage":{"total_tokens":4895,"prompt_tokens":824,"completion_tokens":4071,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":440,"completion_tokens_details":{"reasoning_tokens":4008}},"tokens_in":440,"tokens_out":4071,"duration_ms":25016,"temperature":1.0,"reasoning_tokens":4008,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-10T14:47:29.578022+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Run FL and ERM on the same benchmarks with matched hyperparameter budgets and compare test-set Conditional Value at Risk at high quantiles; if FL does not beat ERM on held-out data in a majority of tasks, the paper's central claim fails. The CIFAR10 experiment in Appendix C is already one such comparison that does not go FL's way.","supporting_citations":[{"cited_title":"On Gradient Descent Ascent for Nonconvex-Concave Minimax Problems","cited_arxiv_id":null,"evidence_quote":"Gives convergence guarantees for nonconvex-strongly-concave minimax problems that justify RFL's quadratically regularized Lagrangian."},{"cited_title":"Convergence Rates in Forward--Backward Splitting","cited_arxiv_id":null,"evidence_quote":"Supplies the linear convergence rate used when the loss geometry is strongly convex."},{"cited_title":"Resilient Constrained Learning","cited_arxiv_id":null,"evidence_quote":"Introduces the slack-variable resilience idea that RFL adapts to a constant-objective feasibility problem."},{"cited_title":"Statistical Learning Theory","cited_arxiv_id":null,"evidence_quote":"Provides the thresholded-loss regression baseline that RFL's clamped-and-squared formulation generalizes."},{"cited_title":"Direct Preference Optimization: Your Language Model is Secretly a Reward Model","cited_arxiv_id":null,"evidence_quote":"Defines the DPO objective used in the preference-optimization experiment."},{"cited_title":"The Implicit Bias of Gradient Descent on Separable Data","cited_arxiv_id":null,"evidence_quote":"Motivates why the optimizer's implicit bias matters when many solutions fit the data, the premise behind FL's algorithmic focus."}],"review_version":1}